Categorical representation theory and applications

分类表示理论及其应用

• 批准号: FT230100489
• 负责人: Dr Daniel Tubbenhauer
• 金额: $ 56.18万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: ARC Future Fellowships
• 财政年份: 2023
• 资助国家: 澳大利亚
• 起止时间: 2023-12-15 至 2027-12-14
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/FT230100489
• 关键词: Categorical; representation; theory; applications

Symmetry is everywhere, and nature is designed symmetrically: Snails make their shells, spiders design their webs, and bees build hexagonal honeycombs, all based on the concept of symmetry. Symmetry is a general principle which plays an important role in various areas of knowledge and perception, ranging from arts to natural sciences and mathematics. The 21th century way of the study of symmetries is categorical representation theory. The project aims are to strengthen this young field by advancing the theory and by finding applications from where its significance arises. The outcome will be new results on categorical representations and this will have benefits within mathematics, cryptography and also in physics/chemistry in the long run.

对称无处不在，大自然是对称设计的：蜗牛制作贝壳，蜘蛛设计它们的网，蜜蜂建造六角形的蜂巢，所有这些都基于对称的概念。对称性是一个普遍的原则，它在从艺术到自然科学和数学的各个知识和感知领域发挥着重要的作用。 21世纪研究对称性的方法是范畴表示论。该项目的目的是通过推进这一理论并在其意义出现的地方找到应用来加强这一年轻的领域。结果将是关于分类表示的新结果，从长远来看，这将在数学、密码学和物理/化学方面带来好处。